Don Quixote's (really Alonso Quijano's) occupation is not named. He is simply a "gentleman" from La Mancha (in the Dedication he is first called "The Ingenious Gentleman Don Quixote of la Mancha") who, having lost his wits, is retired. His occupation, I suppose, is reading:
You must know, then, that the above-named gentleman whenever he was at leisure (which was mostly all the year round) gave himself up to reading books of chivalry with such ardour and avidity that he almost entirely neglected the pursuit of his field-sports, and even the management of his property; and to such a pitch did his eagerness and infatuation go that he sold many an acre of tillageland to buy books of chivalry to read, and brought home as many of them as he could get.
More specifically, Don Quixote is a "hidalgo," a nobleman "who has lost nearly all of his family's wealth but still held on to the privileges and honours of the nobility." These privileges allow him to be indulged by his family, to take up reading for a living, and to command some respect from those below him, like Sancho.